{"id":196366,"date":"2025-03-04T18:25:28","date_gmt":"2025-03-04T18:25:28","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=196366"},"modified":"2025-03-04T18:25:32","modified_gmt":"2025-03-04T18:25:32","slug":"annuities-maria-would-like-to-have-100000-saved-in-her-retirement-account-in-30-years","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/04\/annuities-maria-would-like-to-have-100000-saved-in-her-retirement-account-in-30-years\/","title":{"rendered":"Annuities. Maria would like to have $100,000 saved in her retirement account in 30 years"},"content":{"rendered":"\n<p>Annuities. Maria would like to have $100,000 saved in her retirement account in 30 years. At an interest rate of 8%, how much should she contribute each year?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>Maria should contribute <strong>$882.74<\/strong> each year to reach her goal of <strong>$100,000<\/strong> in 30 years at an interest rate of <strong>8%<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>An annuity is a series of equal payments made at regular intervals. In Maria\u2019s case, she wants to save a certain amount every year to reach her goal of <strong>$100,000<\/strong> in 30 years, assuming an annual interest rate of <strong>8%<\/strong>.<\/p>\n\n\n\n<p>To determine how much Maria should contribute annually, we use the <strong>future value of an annuity formula<\/strong>: FV=PMT\u00d7((1+r)n\u22121r)FV = PMT \\times \\left(\\frac{(1 + r)^n &#8211; 1}{r}\\right)<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>FV<\/strong> = Future Value (<strong>$100,000<\/strong>)<\/li>\n\n\n\n<li><strong>PMT<\/strong> = Annual Contribution (what we need to find)<\/li>\n\n\n\n<li><strong>r<\/strong> = Interest Rate per period (<strong>8% or 0.08<\/strong>)<\/li>\n\n\n\n<li><strong>n<\/strong> = Number of years (<strong>30<\/strong>)<\/li>\n<\/ul>\n\n\n\n<p>Rearranging for <strong>PMT<\/strong>: PMT=FV\u00d7r(1+r)n\u22121PMT = \\frac{FV \\times r}{(1 + r)^n &#8211; 1}<\/p>\n\n\n\n<p>Substituting the values: PMT=100000\u00d70.08(1.08)30\u22121PMT = \\frac{100000 \\times 0.08}{(1.08)^{30} &#8211; 1} PMT=800010.0627\u22121PMT = \\frac{8000}{10.0627 &#8211; 1} PMT=80009.0627PMT = \\frac{8000}{9.0627} PMT\u2248882.74PMT \\approx 882.74<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>Maria needs to <strong>save approximately $882.74 per year<\/strong> to accumulate <strong>$100,000<\/strong> in <strong>30 years<\/strong>. This calculation assumes she makes her contributions at the end of each year and the interest compounds annually.<\/p>\n\n\n\n<p>I will now generate an image to visualize this savings growth over time.<\/p>\n\n\n\n<p>The graph illustrates the growth of Maria&#8217;s retirement savings over 30 years. The blue line represents the total accumulated savings, while the red dashed line marks the target of <strong>$100,000<\/strong>. By consistently contributing <strong>$882.74<\/strong> per year, her savings will gradually increase and reach the goal due to the power of compound interest. Let me know if you need any modifications or further explanations!<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/03\/image-170-1024x637.png\" alt=\"\" class=\"wp-image-196367\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Annuities. Maria would like to have $100,000 saved in her retirement account in 30 years. At an interest rate of 8%, how much should she contribute each year? The correct answer and explanation is: Maria should contribute $882.74 each year to reach her goal of $100,000 in 30 years at an interest rate of 8%. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-196366","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196366","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=196366"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196366\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=196366"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=196366"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=196366"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}